Can an Amateur Lawyer Represent Someone in Court?
Your question is posed as a double negative. A lawyer is another word for an attorney. To answer your question, yes. There is no such phrase as a 'non-lawyer attorney' in law. You are either a lawyer or an attorney. I have no idea where you came up with the term 'non-lawyer attorney.'
Limits on Non-Licensed Professionals in Court
No such thing as a 'non-lawyer attorney' also applies in most cases. A non-lawyer cannot represent clients in court. However, certain exceptions apply. A person can represent themselves in court, but most jurisdictions require that someone representing a litigant be licensed to practice law.
Why Not Represent Your Own Case?
You can represent yourself, but you should not, especially without legal training. It is the perfect excuse for depriving you of an equitable result. They will say that you were a fool for a client no matter how much you study or how solicitous you are to the honorable Judge, who may not even care about you. Lawyers before him are friends who pay money, so don't do it.
Will Lawyers Represent You for Money?
Lawyers will take your money but will not give you a good result when the fix is in. When you are going against the legal establishment, you are pissing into the wind. Just because you can do something doesn't mean you should or that it is a good idea. Your goal should be to put on a show and lose your case representing yourself with no legal training other than what you have obtained from fake entertainment court shows and other television shows which at least have fair technical advisors. You are a one-legged man with both hands tied behind your back in a professional soccer match.
Beginner's Guide to Legal Representation
You do not begin to know the rules, the law, and the facts which hurt or help your case. Going against a lawyer who knows and a judge who does not because of your ignorance is almost certainly suicidal. If you want to win or at least limit the damage caused by a loss, hire a lawyer who has a current license and at least some experience in that court with cases similar to yours.
Conclusion
Yes, you can represent yourself. As they say, someone who plays lawyer represents themselves has a fool for a client. If you need legal help, do consider professional help to ensure you receive fair and effective representation.